Chapter 2.5, Problem 2P

Another equation that has been used to model population growth is the Gompertz equation

$dy/dt=ry\ln (K/y),$ Where $r$ and $K$ are positive constants.

Sketch the graph of $f\left(y\right)$ versus $y$, find the critical points, and determine whether each is asymptotically stable or unstable.

For $0\le y\le K$, determine where the graph of $y$ versus $t$ is concave up and where it is concave down

For each $y$ in $0<y\le K$, show that $dy/dt$, as given by the Gompertz equation, is never less than $dy/dt$, as given by the logistic equation.